Defending the Axioms. On the Philosophical Foundations of Set Theory

Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments. – Contents : Introduction. – 1. The Problem; – 2. Proper Method; – 3. Thin Realism; – 4. Arealism; – 5. Morals.